Exterior power operations on higher $K$-groups via binary complexes

Abstract

We use Grayson's binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a $λ$-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal $λ$-ring on one generator.

35 pages; v2: reference to a correspondence between Deligne and Grothendieck added; v3: referee's comments incorporated, to appear in Annals of K-Theory